You mentioned playing with what you have... and that I can't help you with. But you also mentioned wanting to do well. I can tell you what I think, and maybe if it requires spending money it can be a holiday gift.
I really wished that mechanized marine lists were viable. I really do. Depending on the power level of your local area gaming, they might be passable. But in almost all semi-competitive games, the 4th edition transport rules will just roast you.
Lets go through the list.
Captain... thats fine. A librarian would be your best bet. Chaplain would be better as well if you planned to keep your assault marines. But if passing leadership is important to you then he is a decent buy.
Termies... doesn't get any sweeter
10 man
tac squad... almost got it. step 1 drop the lascannon, step 2 drop the rhino, step three get a drop pod might want to buy a teleport homer on them.. you never know where you'll want it.
5 man
tac squad maybe you can get a couple guys from the 10 man squad and find points to make them 2 x 8 man squads. Drop the razorback.
3 bikes 2 meltas... I would probably prefer plasma guns on these guys, but I don't hate meltas. Ideally, these would be a landspeeder tornado. but it sounds like you knew that.
assault marines.. good against some matchups bad against others... if you are looking to kill infantry, go with a whirlwind (i know you mentioned staying away from "gunline") though. If you want to get stuck in up close, and had some money to spend try a venerable dread in a drop pod. thats always fun
pred... you can drop the extra armor if you want. Its not as essential to be constantly mobile as it would be on a transport. I don't hate extra armor though. Sometimes being able to move 12" after a stunned result can be the difference in claiming an objective or getting a game winning tank-shock. Some people hate predators... A well played pred is a valuable tool. A poorly played pred is about the worst thing you could field. Make sure your expectations match its abilities.
If I were you.. I would do
marine "mechanized"
librarian termie armor fear of darkness
termie command squad 2x assault cannons
venerable dread extra armor drop pod
2x10 man marines plasma gun vet sarge pfist tele homer drop pods
tornado
tornado
pred
no time to check what that points out to... but it might be in the same neighborhood. It might be too cheesy for your group. It might be too much of a hassle for you, since it calls for too many models that you didn't mention owning.
I don't wanna be the guy that says 'rhinos and razorbacks suck, end of story' But I wouldn't feel right if I didn't at least try to steer you away from some pretty underwhelming choices
imo.
good hunting...